"I think in the third, the difference today was we brought another level," said Miller, who won the game with a wrist shot from the faceoff circle.
"I think we have played a lot of the same hockey here for the last six games or so. It's just nice to come out on top. We are doing a lot of good things."
Tyler Toffoli had a goal and an assist for the Canucks, who won for the second time in seven games.
"It's two desperate teams trying to win games, to make the playoffs," said Toffoli, who has six goals and four points in the 10 games since being traded to Vancouver from L.os Angeles on Feb. 17.
"We've been playing playoff hockey ever since I got here. It's that time of the year. It was nice to for us to pull through tonight."
Adam Gaudette, Zack MacEwen and Bo Horvart also scored for Vancouver. Defenseman Alex Edler had two assists, giving him 401 NHL points.
Brock Nelson had a pair of goals for the Islanders, who are mired in a season-long seven-game winless streak (0-4-3). Andrew Ladd and Jordan Eberle also scored for New York. Derick Brassard had two assists.
The win gives the Canucks 78 points and moves them into a tie with Winnipeg and Nashville for the two wild-card playoff spots in the West.
The Islanders have 80 points and remain one point behind Carolina and Columbus for the final two wild-card spots in the East.
It wasn't a win, but the Islanders were happy to get a point and stay in the playoff hunt.
"You worry about the points you can get," New York coach Barry Trotz said. "We put a point on the board. We'll just have to look at trying to get another point or two the next game. Keep doing that and then look up after 82 games and see were we are."
The Islanders scored first, let that lead slip away, but fought back to tie the game three times.
"I thought we did a pretty good job a couple times battling back," said Nelson, who has 26 goals. "We need that right now, especially the way things are going for us.
"It seems like we're close, but we've just got to find that puck or that play to kind of get us over the hump and turn it around."
Canuck goaltender Thatcher Demko, who had a career-high 45 saves, came up big several times. He stopped Matthew Barzal and Eberle during an Islanders' 5-on-3 power play in the first period. In the second, he got a pad on a Barzal shot on a 2-on-1.
"I'm learning a lot through this process," said Demko, who is playing in place of the injured Jakob Markstrom. "Down the stretch, we are going to have to be really sharp as a group and individually.
"It was a good win tonight."
New York goalie Semyon Varlamov stopped 30 shots.
Nelson tied the game at 4:32 of the third when he collected a loose puck and batted it past Demko. His second goal of the night came just two seconds after the Canucks had killed a penalty.
Vancouver scored late in the second period for a 4-3 lead after the teams were tied 2-2 after 20 minutes.
MacEwen put the Canucks up 3-2 at 2:14 of the second when he tipped an Edler shot past Varlamov. It was MacEwan's third goal in three games.
Nelson tied the game at 17:00 when he got behind the Vancouver defense and beat Demko with a backhand on the short side.
Horvat gave Vancouver the lead again on a power play with 2:09 remaining. He took a pass from Toffoli from behind the goal line and shot the puck through Varlamov.
The teams combined for three goals in the first 2:41 of the opening period.
Just 96 second had ticked off the clock when Ladd tipped in a shot by Josh Bailey.
Vancouver struck just 21 seconds later when Gaudette deflected a shot from Edler.
Vancouver went ahead at 2:41 when Toffoli took a cross-ice pass from Elias Pettersson and put a shot over Varlamov's glove.
Eberle made it 2-2 with just 59 seconds remaining when he moved through the Canuck defense and lifted a backhand past Demko.
Forward Brock Boeser returned to the Canucks lineup after missing 12 games with a fractured rib cartilage. . The return of Boeser resulted in Loui Eriksson being a healthy scratch. . Canuck goaltender Jacob Markstrom, who has missed eight games with a knee injury, skated Tuesday morning. . Ladd's goal was his first since Oct. 30, 2018. He has only played 21 games in that time due to injuries. . Islander defenseman Johnny Boychuk remains day to day with an eye injury.
Islanders: At Calgary Flames on Thursday.
Canucks: At Arizona Coyotes on Thursday.
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Miller's shootout goal leads Canucks to victory
J.T. Miller score the only goal in the shootout giving the Canucks the victory over the Islanders.